1. Field of the Invention
The present invention relates to a method of determining all of the 2D or 3D components of an absolute permeability tensor of a porous medium sample and/or allowing scaling of heterogeneous permeability fields, from data measured in the laboratory or from underground zone permeability maps provided by geologists.
2. Description of the Prior Art
Laboratory measurement of the permeability of rocks are a key stage in oil reservoir, aquifer, civil engineering surveys, or even the study of catalysts used in the chemical industry. If a medium exhibits obvious anisotropy directions, the experimenter will try to respect them during measurement survey. In other words, the experimenter will position along proper axes of the permeability tensor. There are cases where this direction is not given beforehand and the tensor therefore has to be determined a priori without preconceived ideas. It can also turn out that the rock samples have not been cored in the right directions; furthermore, the proper axes of the tensor are not necessarily aligned with the bedding exhibited by some rock samples.
It is therefore particular useful to have direct measurements of all the components of the tensor, or at least to estimate the possible anisotropy thereof.
A method of determining a permeability tensor of a rock sample from measurements allowing estimation of, with sufficient accuracy, the mean pressures around a sample placed in a permeameter suited to the measurements thereof is described for example in the following publication:    Renard P. “Laboratory Determination of the Full Permeability Tensor” JGR 106, B11 2001 pp 26 443–26 451.
Another known method of determining a permeability tensor wherein flows which are made deliberately tortuous by changes in the boundary conditions of the injection faces are created in the sample and wherein an inverse problem is solved is for example described in the following publication:    Bernabé Y.: “On the Measurement of Permeability in Anisotropic Rocks” in “Fault Mechanics and Transport Properties of Rocks” edited by B. Evans and T F Wong pp 147–167, Academic San Diego 1992.
In order to be implemented, the known methods require substantial changes in the flow conditions, which makes them costly and difficult to be applied in practice.
Within the context of upscaling, well-known to reservoir engineers, laboratory experiments are replaced by the results of a “fine” numerical simulation on the heterogeneous medium, in order to replace it by an equivalent homogeneous medium whose permeability tensor is for example denoted by Keff. In the case of an anisotropic medium, the fine reference simulation is generally performed by considering periodic boundary conditions. Most authors wrongly consider that these are the only conditions allowing obtaining all the elements of the tensor Keff.
As shown in the description hereafter, a suitable interpretation of a numerical simulation of the same permeameter can provide this information. The boundary conditions applied in a permeameter can be more realistic in the case where the large-scale flow is constrained by clay barriers. Furthermore, the comparison between the two resulting tensors can provide information on the scale of the Representative Elementary Volume (REV).